Bowser had no hair in the original SMB and Japanese SMB2, which explains why he has no hair in the cartoons. I've only seen episodes of SMW and SMB3, so I don't know what the characters look like in the Super Show.
Oh, and Link had several different incarnations, so it's obvious why they have different looks in different games, etc. If you follow a chronological timeline of he series like I do, Link first has blond hair, and it darkens in each new incarnation of Link, So, by the time we are around the LoZ-AoL era, we see Link with brown hair.
That's just my theory, though.